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Understanding 9/11xxxv, 288 p. : 24 cm
Includes bibliographical references (p. 279-282) and index
1. Classical Algebra -- 2. The Fundamental Theorem of Algebra -- 3. Factorization of Polynomials -- 4. Field Extensions -- 5. Simple Extensions -- 6. The Degree of an Extension -- 7. Ruler-and-Compass Constructions -- 8. The Idea Behind Galois Theory -- 9. Normality and Separability -- 10. Counting Principles -- 11. Field Automorphisms -- 12. The Galois Correspondence -- 13. A Worked Example -- 14. Solubility and Simplicity -- 15. Solution by Radicals -- 16. Abstract Rings and Fields -- 17. Abstract Field Extensions -- 18. The General Polynomial -- 19. Regular Polygons -- 20. Finite Fields -- 21. Circle Division -- 22. Calculating Galois Groups -- 23. Algebraically Closed Fields -- 24. Transcendental Numbers
Includes bibliographical references (p. 279-282) and index
1. Classical Algebra -- 2. The Fundamental Theorem of Algebra -- 3. Factorization of Polynomials -- 4. Field Extensions -- 5. Simple Extensions -- 6. The Degree of an Extension -- 7. Ruler-and-Compass Constructions -- 8. The Idea Behind Galois Theory -- 9. Normality and Separability -- 10. Counting Principles -- 11. Field Automorphisms -- 12. The Galois Correspondence -- 13. A Worked Example -- 14. Solubility and Simplicity -- 15. Solution by Radicals -- 16. Abstract Rings and Fields -- 17. Abstract Field Extensions -- 18. The General Polynomial -- 19. Regular Polygons -- 20. Finite Fields -- 21. Circle Division -- 22. Calculating Galois Groups -- 23. Algebraically Closed Fields -- 24. Transcendental Numbers
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